JIPMAT 2025 (QA) - Let x be the least number which when divided by 8, 12, 20, 28, 35 leaves a remainder of 5 in each case, then the sum of digits of x is : | PYQs + Solutions

JIPMAT 2025

Number System

HCF & LCM

Hard

Let $x$ be the least number which when divided by $8, 12, 20, 28, 35$ leaves a remainder of $5$ in each case, then the sum of digits of $x$ is :

✅ Correct Option: 1

To find such least number, we need to find the LCM of the given numbers and add 5 to the LCM.

LCM of

8, 12, 20, 28, 35

\begin{array}{c|ccc} 2 & 8, & 12, & 20, & 28, & 35 \newline \hline 2 & 4, & 6, & 10, & 14, & 35 \newline \hline 7 & 2, & 3, & 5, & 7, & 35 \newline \hline 5 & 2, & 3, & 5, & 1, & 5 \newline \hline & 2, & 3, & 1, & 1, & 1 \end{array}

LCM

= 2 \times 2 \times 2 \times 3 \times 5 \times 7 = 840

\therefore

Least number which when divided by

8,12,20,28,35

leaves a remainder of 5 in each case is

840+5 = 845

Sum of digits of

845 = 8+4+5 = 17